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Which of the following factors typically influence the choice of sources of funds for a business?

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Important Questions on Linear Inequalities

EASY

Mathematics>Algebra>Linear Inequalities>Types of Inequalities

The Number of ways of choosing

10

objects out of

31

objects of which

10

are identical and the remaining

21

are distinct, is:

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

Consider a class of

5

girls and

7

boys. The number of different teams consisting of

2

girls and

3

boys that can be formed from this class, if there are two specific boys

A

and

B,

who refuse to be the members of the same team, is:

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

The value of

\sum_{r = 1}^{10} r \cdot \frac{{}^{n}C_{r}}{{}^{n}C_{r - 1}}

is equal to

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

Suppose that

20

pillars of the same height have been erected along the boundary of circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is:

MEDIUM

Mathematics>Algebra>Linear Inequalities>Types of Inequalities

A committee of

11

member is to be formed from

8

males and

5

females. If

m

is the number of ways the committee is formed with at least

6

males and

n

is the number of ways the committee is formed with at least

3

females, then

EASY

Mathematics>Algebra>Linear Inequalities>Types of Inequalities

There are

m

men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by

84

, then the value of

m

is :

HARD

Mathematics>Algebra>Linear Inequalities>Types of Inequalities

If in a regular polygon the number of diagonals is

54

, then the number of sides of this polygon is:

HARD

Mathematics>Algebra>Linear Inequalities>Types of Inequalities

{\sum_{i = 1}^{20} (\frac{^{20} C_{i - 1}}{^{20} C_{i} +^{20} C_{i - 1}})}^{3} = \frac{k}{21},

then

k

equals

EASY

Mathematics>Algebra>Linear Inequalities>Types of Inequalities

In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls (i.e., when they are in contact).

(b) Total linear momentum? Give reason for your answer in each case.

EASY

Mathematics>Algebra>Linear Inequalities>Types of Inequalities

A truck and a car are moving with same kinetic energy. Both are brought to rest by applying the same retarding force.

S_{1}

is the distance travelled by truck before coming to rest and

S_{2}

is the distance travelled by the car before coming to rest.

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

A bullet of mass $m$ fired at $30 °$ to the horizontal leaves the barrel of the gun with a velocity $v .$ The bullet hits a soft target at a height $h$ above the ground while it is moving downward and emerges out with half the kinetic energy it had before hitting the target. Which of the following statements are correct in respect of bullet after it emerges out of the target?

EASY

Mathematics>Algebra>Linear Inequalities>Types of Inequalities

When an ideal gas is compressed adiabatically, temperature rises and the molecules on the average have more kinetic energy than before. The kinetic energy increases

EASY

Mathematics>Algebra>Linear Inequalities>Types of Inequalities

A light and heavy body have equal kinetic energy. Which has greater momentum?

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls (i.e., when they are in contact).

(a) Kinetic energy.

Give reasons for your answer.

EASY

Mathematics>Algebra>Linear Inequalities>Types of Inequalities

A machine, which is

75 %

efficient, uses

12 J

of energy in lifting up a

1 kg

mass through a certain distance. The mass is then allowed to fall through that distance. The velocity at the end of its fall is (in

{ms}^{- 1}

)

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Suppose the average mass of raindrops is

3 \times 10^{- 5} kg

and their average terminal velocity

9 {ms}^{- 1}

. Calculate the energy transferred by rain to each square metre of the surface at a place which receives

100 cm

of rain in a year.

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Mathematics>Algebra>Linear Inequalities>Types of Inequalities

An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy

10 keV

, and the second with

100 keV

. Which is faster, the electron or the proton? Obtain the ratio of their speeds. (electron mass

= 9.11 \times 10^{- 31} kg

, proton mass

= 1.67 \times 10^{- 27} kg

1 eV = 1.60 \times 10^{- 19} J

)

EASY

Mathematics>Algebra>Linear Inequalities>Types of Inequalities

If a man speeds up by

1 m s^{- 1}

, his KE increase by

44 %

. His original speed in

m s^{- 1}

EASY

Mathematics>Algebra>Linear Inequalities>Types of Inequalities

Two bodies

A

and

B

have masses

20 k g a n d 5 kg

respectively. Each one is acted upon by a force of

4 kgf

. If they acquire the same kinetic energy in time

t_{A}

and

t_{B}

respectively. Then the ratio of

\frac{t_{A}}{t_{B}}

is
(Assume

g = 10 m s^{- 2}

)

EASY

Mathematics>Algebra>Linear Inequalities>Types of Inequalities

In a ballistics demonstration a police officer fires a bullet of mass

50 g

with speed

200 {ms}^{- 1}

on soft plywood of thickness

2 cm

. The bullet emerges with only

10 %

of its initial kinetic energy. The emergent speed of the bullet is

Which of the following factors typically influence the choice of sources of funds for a business?

Important Questions on Linear Inequalities

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